This process is fairly simple, to do this you need to upload the favicon.ico to the Default Folder in the File Library section. The name of the file has to be "favicon.ico".
Below is an example of this:
If you do not see the image change check these things:
1. Make sure it is in the default folder.
2. Make sure the file name is exactly as shown above.
3. Try clearing your cookies and cache on the browser you are using.